2026 IGCSE Additional Mathematics May/June 0606/13 Q9

2026 IGCSE Additional Mathematics May/June 0606/13 Q9

8 marks

A circle has centre \((3,1)\) and radius \(1\).

A line has equation \(2y+x=c\), where \(c\) is a constant.

  1. Given that the line is a tangent to the circle, find the two possible values of \(c\).[7]
  2. When \(c\) takes a value between the two values found in 9(a), state the relationship between the line and the circle.[1]

Solution:

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Answer:(a) \(c=5\pm\sqrt5\) (b) The line meets the circle at two distinct points.

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